Question

Solve the following question and mark the most appropriate option.
x is a natural number between 1 and 20, both inclusive, such that

1. If x is less than 10, then it is even.
2. If x is not divisible by 3, then it is prime.
3. If x is not a factor of 60, then it is a factor of 102.
4. If x, when divided by 7, leaves a remainder greater than 4, then it is greater than 14.
5. If one less than x is a perfect square, then the reciprocal of x is less than 4/7.
6. If one more than x is a perfect square, then x is not divisible by 5.

What is the value of x?

पर्याय

• 2

• 3

• 5

• 8

Answer 1

From the first condition, if x is less than 10, then x = 2, 4, 6 or 8, otherwise it is 10, 11, 12, ..., 20.
From the second condition, if x is divisible by 3, then x = 6, 9, 12, 15 or 18, otherwise it is 2, 5, 7, 11, 13, 17 or 19.
From the third condition, if x is a factor of 60, then x = 1, 2, 3, 4, 5, 6, 10, 12, 15 or 20, otherwise it is 17.
From the fourth condition, if x when divided by 7 leaves a remainder greater than 4, then x = 19 or 20, otherwise it is 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 15,16, 17, 18
From the fifth condition, if x – 1 is a perfect square, then x = 2, 5, 10 or 17, otherwise it is 1, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20.
From the sixth condition, if x + 1 is a perfect square, then x = 3 or 8, otherwise it is 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, ..., 20.
The only value that satisfies all of the above conditions is x = 2.